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In this work, using the inversion coefficients and some connection coefficients between some polynomial sets, we give explicit representations of the moments of all the orthogonal polynomials belonging to the Askey–Wilson scheme. Generating functions for some of these moments are also provided. [ABSTRACT FROM AUTHOR]

Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n , the P n satisfy the orthogonality relation 〈 L , P n P m 〉 = 0 , n ≠ m , 〈 L , P n P n 〉 ≠ 0 , n ≥ 0 and L satisfies the Pearson equation D x ( ϕ L ) = S x ( ψ L ) , where ϕ is a non zero polynomial and ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials. [ABSTRACT FROM AUTHOR]